As graphics processing applications become increasingly more powerful, memory requirements associated with the execution of graphics instructions have correspondingly increased. To support such applications, processors supporting graphics operations may utilize additional memory outside the processor in carrying out graphics processing instructions. In a modern multithreaded processor capable of supporting a large number of active threads of execution, fixedly assigning a portion of outside memory to each thread of execution can easily result in the use of an exorbitant amount of outside memory. Nevertheless, a processor may need to capitalize on performance gains achieved through use of outside memory allotted to graphics processing on a per thread basis. Accordingly, there exists a compelling need for a technique that allows a multithreaded processor to take advantage of outside memory for execution of threads without consuming excessive allocations of such outside memory.